If tan x = 2 , and x is in quadrant 1

Question

Find exact values of

1) sin(2x)

2)cos(2x)

3)tan2(x)

Answer 1

If tan x = 2, then cos x = (1/5)sqrt(5) and sin x = (2/5)sqrt(5)

sin 2x = 2 sin x cos x = 4/5

cos 2x = (cos x)^2 - (sin x)^2 = -3/5

(tan x)^2 = 4